We obtain results of existence and multiplicity of solutions for the second-order equation x'' + q(t)g(x) = 0 with x(t) defined for all t in ]0,1[ and such that x(t) goes to infinity as tends to 0+ and to 1-. We assume g having superlinear growth at infinity and q(t) possibly changing sign on [0, 1].
Boundary blow-up for differential equations with indefinite weight / Mawhin, J.; Papini, Duccio; Zanolin, Fabio. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 188:1(2003), pp. 33-51. [10.1016/S0022-0396(02)00073-6]
Boundary blow-up for differential equations with indefinite weight
PAPINI, Duccio;
2003
Abstract
We obtain results of existence and multiplicity of solutions for the second-order equation x'' + q(t)g(x) = 0 with x(t) defined for all t in ]0,1[ and such that x(t) goes to infinity as tends to 0+ and to 1-. We assume g having superlinear growth at infinity and q(t) possibly changing sign on [0, 1].
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